001 earth pressure_part 1

8/15/2019 001 Earth Pressure_Part 1

1/18

Earth Pressures


2/18

Analysis and Design

of Earth Retaining Structures

• Distribution of vertical and lateral earth

pressures must be estimated

• Magnitude of earth pressure depends on

state of strain in the soil behind the

structure


3/18

Earth Pressure Theory

• The following 3 states are defined:

- At rest state: elastic equilibrium with no lateral

strain

- Active state: plastic equilibrium with lateral

expansion

- Passive state: plastic equilibrium with lateral

compression


4/18

At-rest State

• Lateral effective stress, sh' = Ko sv'

• sv' = sv – u• Ko = coefficient of earth pressure at rest

sh’

sv’

Groundlevel

z


5/18

Value of Ko

• For normally consolidated soils,

Ko = 1 – sinf'

• For overconsolidated soils,

Ko = (1 – sinf' ) (OCR)0.5

• From elastic theory,

Ko =

1


6/18

Rankine’s Earth Pressure Theory

• In Rankine’s method, it is assumed that there is no

friction or adhesion between soil and the back of the

retaining structure. Therefore, the normal stress acting

on the retaining structure will be a principal stress. If the

back of the retaining structure is vertical and the soilsurface horizontal, the vertical and horizontal stresses

throughout the retained soil mass will be principal

stresses.

• The horizontal stress can be calculated from the Mohr-

Coulomb failure criterion.


7/18

Active Earth Pressure: Granular Soil

sv’

sh’

z

A

B

• Initially, no movement of boundary AB

At-rest state

sv’ = z, assuming u = 0

sh’ = Ko sv

’ = Ko z

• Boundary AB moves away from element,

No change in sv’

Decrease in sh’ until it reaches a

minimum value, sha’ , at failure


8/18

Active Earth Pressure: Rankine’s Theory

Granular Soil (c' = 0)

s'

Decreasing h’

At-rest state

Active state

sha’

'σK 'σ vaha

)2/'45(tan

'sin1

'sin1 pressureearthactiveof tcoefficienK 2a f

f

f


9/18

Passive Earth Pressure: Granular Soil

sv’

sh’

z

A

B

• Boundary AB moves towards element,

No change in sv’

Increase in sh’ until it reaches amaximum value, shp’ , at failure


10/18

Passive Earth Pressure: Rankine’s Theory

Granular Soil

s’sv’

increasing sh’

shp’

c' = 0

At-rest statePassive state


11/18

Passive Earth Pressure: Rankine’s Theory

Granular Soil (c' = 0)

'σK 'σ v php

)2/'45(tan'sin1

'sin1

pressureearth passiveof tcoefficienK 2

p f f

f


12/18

Earth Pressure Theory:

Orientation of Failure Plane

• In the active case, the

failure plane is inclined at an

angle of (45o + f'/2) to the

horizontal.

• In the passive case, the

failure plane is inclined at an

angle of (45o - f'/2) to the

horizontal.


13/18

Earth Pressure Theory:

Orientation of Failure Plane

• In the active case, the failure plane is inclined at an angle of (45o +

f'/2) to the horizontal.

• In the passive case, the failure plane is inclined at an angle of (45o -

f'/2) to the horizontal.


14/18

Mobilisation of Earth Pressure with Movement

• Significantly higher movement is required to mobilise full passive pressure

than to mobilise active pressure

Towards

soil

Away

from soil

Kp

Ko

Ka


15/18

Earth Pressure: c' – f' soil

Rankine-Bell Equations

• Active case:

• Passive case: pv php K 2c''σK 'σ

c' s' tan f'

avaha K 2c''σK 'σ

sv'sha' shp' s'


16/18

Earth Pressure: c' – f' soil

Rankine-Bell Equations

• Active case

– When c‘ is greater than zero, sha'

is zero at a specific depth, zo.

– Within a depth zo, active earth

pressure is negative.

aK 2c'

ava K 2c''σK

zo


17/18

Earth Pressure Distribution

• Effect of

– Groundwater level

– Surcharge

– Stratified soil

– Sloping ground


18/18

Influence of Sloping Ground

'cos-coscos

'cos-cos-cosK

22

22

a

f

f

'cos-coscos

'cos-coscosK 22

22

p

f

f

H H

3

H

Active pressure, pa = Ka sv' cos

Where sv' = Hcos

Active force, F A = Ka H2 cos

Passive pressure, pp = Kp sv' cos

Passive force, FP = Kp H2 cos

21

2

1

F A

001 earth pressure_part 1

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